[B! çµ±è¨ˆ] bluesky0804ã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

bluesky0804 id:bluesky0804

çµ±è¨ˆã«é–¢ã™ã‚‹bluesky0804ã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (12)

${{author_name}}$

{{{comment_expanded}}}

{{label}}

{{#is_bookmark}}ãƒªã‚¹ãƒˆ{{/is_bookmark}}{{^is_bookmark}}ãƒªãƒ³ã‚¯{{/is_bookmark}}

${{author_name}}$
{{author_name}}{{created}}
{{ #comment }}{{ comment }}{{ /comment }}
- {{ label }}

${{author_name}}$

{{{comment_expanded}}}

{{label}}

{{#is_bookmark}}ãƒªã‚¹ãƒˆ{{/is_bookmark}}{{^is_bookmark}}ãƒªãƒ³ã‚¯{{/is_bookmark}}

æ–™ç†ãƒãƒˆãƒ«æ¼«ç”»ã§å…ˆã«çš¿ã‚’å‡ºã—ãŸå ´åˆã®å‹çŽ‡ | ãƒžãƒ³ãƒé€šä¿¡
ã“ã‚“ã«ã¡ã¯ã€‚å›½åºœç”ºæ€’å…ï¼ˆã“ã†ã¾ã¡ã¬ã‚“ã˜ï¼‰ã§ã™ã€‚ æ–™ç†ãƒãƒˆãƒ«æ¼«ç”»ã§ã€ã¾ã“ã¨ã—ã‚„ã‹ã«èªžã‚‰ã‚Œã¦ã„ã‚‹å™‚ã¯ã”å˜çŸ¥ã§ã—ã‚‡ã†ã‹ã€‚ ãã†ã€ã€Œå¾Œæ”»ã§çš¿ã‚’å‡ºã—ãŸæ–™ç†äººãŒå‹ã¤ã€ã§ã™ã€‚ ç¢ºã‹ã«ã€æ¼«ç”»ã®æ§‹é€ ã‚’è€ƒãˆã‚Œã°ã€å¾Œæ”»ãŒæœ‰åˆ©ã‹ã‚‚ã—ã‚Œã¾ã›ã‚“ã€‚ æœ€åˆã«ã™ã”ã„æ–™ç†ãŒå‡ºã¦ã€å¾Œã‹ã‚‰ãã‚Œãªã‚Šã®æ–™ç†ãŒå‡ºã‚‹å±•é–‹ã ã¨ã€ å°»ã¤ã¼ã¿ãªã‚¤ãƒ¡ãƒ¼ã‚¸ã«ãªã£ã¦ã—ã¾ã„ã¾ã™ã‚‚ã‚“ãã€‚ ãŸã ã€ä¸€ã¤ç´å¾—ã®ã„ã‹ãªã„ã“ã¨ãŒã‚ã‚Šã¾ã™ã€‚ ãã‚Œã¯ã€å¾Œæ”»ãŒæœ‰åˆ©ãªã“ã¨ã‚’ãƒ‡ãƒ¼ã‚¿ã¨ã—ã¦ç¤ºã—ãŸäººãŒã„ãªã„ã¨ã„ã†ç‚¹ã§ã™ã€‚ ã‚‚ã—ã‹ã—ãŸã‚‰ã€å¾Œæ”»ãŒå‹ã£ãŸã¨ãã®å°è±¡ãŒå¼·ã„ã ã‘ã§ã€å…ˆæ”»ã‚‚ãã‚Œãªã‚Šã«å‹ã£ã¦ã„ã‚‹ã‹ã‚‚ã—ã‚Œã¾ã›ã‚“ã€‚ ã˜ã‚ƒã‚ã€ã©ã†ã™ã‚‹ã‹ã€‚ è‡ªåˆ†ã§æ˜Žã‚‰ã‹ã«ã™ã‚‹ã—ã‹ãªã„ã§ã—ã‚‡ã†ã€‚ ã¨ã„ã†ã“ã¨ã§ã€æ–™ç†ãƒãƒˆãƒ«æ¼«ç”»ã§å…ˆæ”»ã§çš¿ã‚’å‡ºã—ãŸå ´åˆã®å‹çŽ‡ã‚’èª¿æŸ»ã—ã¾ã—ãŸã€‚ ä»¥ä¸‹ã€ãƒ¬ã‚®ãƒ¥ãƒ¬ãƒ¼ã‚·ãƒ§ãƒ³ã§ã™ã€‚ â‘ é›†è¨ˆã¯ã€ï¼‘å¯¾ï¼‘ã®å¯¾æ±ºã«é™ã‚‹ â€»ï¼‘ã€€ï¼”äººã®ä¸ã§èª°ãŒä¸€ç•ªã‹ã¨ã„ã£ãŸã€å…ˆæ”»å¾Œæ”»ãŒæ›–æ˜§ãªå½¢å¼ã¯å«ã‚ãªã„ â€»ï¼’
bluesky0804 2017/09/21
è‰

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
æœ€ã‚‚æˆåŠŸã—ã¦ã„ã‚‹äººã¯éŽå¤§è©•ä¾¡ã•ã‚ŒãŒã¡ã ãŒé‹ã«ã‚ˆã‚‹è¦ç´ ãŒå¤§ãã„ã€‚æœ¬å½“ã«å¦ã¶ã¹ãå¯¾è±¡ã¯2ä½ã‚„3ä½ï¼ˆè‹±ç ”ç©¶ï¼‰ | ã‚«ãƒ©ãƒ‘ã‚¤ã‚¢
äººç”Ÿã®å‹è€…ã§ã‚ã‚‹ä¸–ç•Œæœ€é«˜ã®å¯Œè£•å±¤ã¯ã€ã¨ã‹ããŠæ‰‹æœ¬ã¨ã—ã¦å‚è€ƒã«ã™ã‚‹ã¹ãã ã¨æ€ã‚ã‚ŒãŒã¡ã ã€‚ã—ã‹ã—è‹±ã‚¦ã‚©ãƒ¼ãƒªãƒƒã‚¯ãƒ»ãƒ“ã‚¸ãƒã‚¹ã‚¹ã‚¯ãƒ¼ãƒ«ã®ãƒã‚§ãƒ³ã‚¦ã‚§ã‚¤ãƒ»ãƒªãƒ¥ãƒ¼ï¼ˆChengwei Lau ï¼‰æ°ã¯ã€ã€Œå½¼ã‚‰ãŒå„ªã‚Œã¦ã„ã‚‹ã“ã¨ã¯ç¢ºã‹ã ã‚ã†ãŒã€æœ€é«˜ã®ã‚¹ã‚ãƒ«ã‚’æŒã£ã¦ã„ã‚‹ã‹ã¨ã„ãˆã°å¿…ãšã—ã‚‚ãã†ã¨ã¯è¨€ãˆã¾ã›ã‚“ã€ã¨è©±ã™ã€‚ å‹è€…ã«ãªã‚‹ã‹ã©ã†ã‹ã¯é‹ãŒå¤§ããå·¦å³ã™ã‚‹ ãƒªãƒ¥ãƒ¼æ°ã‚‰ãŒ2012å¹´ã«ã€ŽProceedings of the National Academy of Sciencesã€ã§ç™ºè¡¨ã—ãŸç ”ç©¶ã«ã‚ˆã‚‹ã¨ã€çªå‡ºã—ãŸãƒ‘ãƒ•ã‚©ãƒ¼ãƒžãƒ³ã‚¹ã‚’ç¤ºã™äººç‰©ãŒæœ€ã‚‚å„ªã‚ŒãŸã‚¹ã‚ãƒ«ã‚’èº«ã«ã¤ã‘ã¦ã„ã‚‹ã¨ã„ã†è¦‹è§£ã¯é–“é•ã„ã ã¨ã„ã†ã€‚ãã®ç†ç”±ã¯çªå‡ºã—ãŸãƒ‘ãƒ•ã‚©ãƒ¼ãƒžãƒ³ã‚¹ã¯ã—ã°ã—ã°ä¾‹å¤–çš„ãªçŠ¶æ³ã§ç”Ÿã˜ã‚‹ã‚‚ã®ã ã‹ã‚‰ã ã€‚ ã™ãªã‚ã¡æœ€é«˜ã®ãƒ‘ãƒ•ã‚©ãƒ¼ãƒžãƒ³ã‚¹ã‚’ç¤ºã—ãŸäººç‰©ã¯ã€ã—ã°ã—ã°æœ€ã‚‚é‹ã«æµã¾ã‚ŒãŸäººç‰©ã§ã‚ã‚‹ã¨ã„ã†ã“ã¨ã ã€‚å½¼ã‚‰ã¯å¯Œã‚ã‚‹è€…ãŒã•ã‚‰ã«å¯Œã‚ã‚‹ãƒ€ã‚¤ãƒŠãƒŸã‚¯ã‚¹ã®æ©æµã‚’å—ã‘ã€æœ€åˆ
bluesky0804 2017/09/14
ãƒ™ã‚¤ã‚ºã®å®šç†å¾©ç¿’ã—ã¨ã„ã¦ã€‚

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
ã€Œãƒ™ãƒ«ãƒŒãƒ¼ã‚¤è©¦è¡Œã€ã®è‹±èªžãƒ»è‹±èªžä¾‹æ–‡ãƒ»è‹±èªžè¡¨ç¾ - Weblioå’Œè‹±è¾žæ›¸
Weblioè‹±å’Œå¯¾è¨³è¾žæ›¸ã¯ãƒ—ãƒã‚°ãƒ©ãƒ ã§æ©Ÿæ¢°çš„ã«æ„å‘³ã‚„è‹±èªžè¡¨ç¾ã‚’ç”Ÿæˆã—ã¦ã„ã‚‹ãŸã‚ã€ä¸é©åˆ‡ãªé …ç›®ãŒå«ã¾ã‚Œã¦ã„ã‚‹ã“ã¨ã‚‚ã‚ã‚Šã¾ã™ã€‚ã”äº†æ‰¿ãã ã•ã„ã¾ã›ã€‚
bluesky0804 2017/09/13
Bernoulli trials

è‹±èªž

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
Hoeffdingã®ä¸ç‰å¼ - æ©Ÿæ¢°å¦ç¿’ã®ã€Œæœ±é·ºã®æœWikiã€
Hoeffdingã®ä¸ç‰å¼ (Hoeffding's inequality)â€ $n$å€‹ã®ç‹¬ç«‹ãªç¢ºçŽ‡å¤‰æ•°$X_1,\cdots,X_n$ã®å€¤åŸŸã¯$[a_i,b_i]$ã¨ã™ã‚‹ï¼Ž$S_n=X_1+\ldots+X_n$ ã¨ã—ï¼Œã‚ã‚‹æ£æ•° $\epsilon$ ã«ã¤ã„ã¦æ¬¡ã®Hoeffdingã®ä¸ç‰å¼ãŒæˆç«‹ï¼Ž \[\Pr[S_n - \mathrm{E}[S_n]\ge n\epsilon]\le \exp\biggl(-\frac{2n^2\epsilon^2}{\sum_{i=1}^n(b_i-a_i)^2}\biggr)\] ãŸã ã—ï¼Œ$\mathrm{E}[\cdot]$ ã¯æœŸå¾…å€¤ï¼Ž ç¢ºçŽ‡åˆ†å¸ƒã«ä¾å˜ã›ãšã«æˆç«‹ã™ã‚‹ç‚¹ãŒä¾¿åˆ©ï¼Ž -- ã—ã¾ã—ã¾ â†‘
bluesky0804 2017/09/13
ãƒ˜ãƒ•ãƒ‡ã‚£ãƒ³ã‚°ã¨èªã‚€ã€‚

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
Hoeffding's inequality - Wikiwand
bluesky0804 2017/09/13
much tighter than Markov and Chebyshevâ€™s inequality. (Used to show SLLN?)

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
ã‚¢ãƒ¤ãƒ¡å±ž - Wikiwand
bluesky0804 2017/09/13
ã‚¢ãƒ¤ãƒ¡å±žï¼ˆã‚¢ãƒ¤ãƒ¡ãžãã€Irisï¼‰ï¼šçµ±è¨ˆå¦è€…ã‚„ãã®ä»–ã®äººã€…ã«ã‚ˆã£ã¦éª¨ã®é«„ã¾ã§ã—ã‚ƒã¶ã‚‰ã‚ŒãŸå“€ã‚Œãªæ¤ç‰©ç¨®

è‹±èªž

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
Iris flower data set - Wikiwand
The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher in his 1936 paper The use of multiple measurements in taxonomic probl ems as an example of linear discriminant analysis.[1] It is sometimes called Anderson's Iris data set because Edgar Anderson collected the data to quantify the morphologic vari
bluesky0804 2017/09/13
a typical test case for many statistical classification techniques in machine learning such as support vector machines.ï¼šSVMã¯classificationã®ä¸€ã¤ã€‚

çµ±è¨ˆ

æ©Ÿæ¢°å¦ç¿’
ãƒªãƒ³ã‚¯
æœ‰æ„æŠ½å‡ºæ³•(ã‚†ã†ã„ã¡ã‚…ã†ã—ã‚…ã¤ã»ã†)ã¨ã¯ï¼Ÿ æ„å‘³ã‚„ä½¿ã„æ–¹ - ã‚³ãƒˆãƒãƒ³ã‚¯
æ¨™æœ¬èª¿æŸ»ã«ãŠã‘ã‚‹æ¨™æœ¬æŠ½å‡ºæ³•ã®ä¸€ã¤ã§ï¼Œæ¯é›†å›£ã‚’ã§ãã‚‹ã ã‘ã‚ˆãä»£è¡¨ã™ã‚‹ã‚ˆã†ãªæ¨™æœ¬ã‚’æ„å›³çš„ã«é¸ã³å‡ºã™æ–¹æ³•ã€‚æ¨™æœ¬ã®æŠ½å‡ºãŒï¼Œã¾ã£ãŸãç ”ç©¶è€…ã®ä¸»è¦³ã«ä¾å˜ã™ã‚‹å ´åˆã‚‚ã‚ã‚‹ãŒï¼Œã‚ˆã‚Šç§‘å¦çš„ãªæ–¹æ³•ã§ã¯ï¼Œèª¿æŸ»ã—æŽ¨å®šã—ã‚ˆã†ã¨ã™ã‚‹èª¿æŸ»é …ç›®ã¨ç›¸é–¢ã®é«˜ã„ï¼Œ1å€‹ã‚ã‚‹ã„ã¯æ•°å€‹ã®æ¨™è˜ã‚’ã‚³ãƒ³ãƒˆãƒãƒ¼ãƒ«ã¨ã—ã¦å®šã‚ï¼Œã“ã®ã‚³ãƒ³ãƒˆãƒãƒ¼ãƒ«ã«é–¢ã—ã¦ï¼Œæ¨™æœ¬ãŒæ¯é›†å›£ã¨åŒã˜å¹³å‡ï¼ŒåŒã˜æ¯”çŽ‡ã‚’ç¤ºã™ã‚ˆã†ã«æŠ½å‡ºã™ã‚‹ã€‚ã“ã®æ–¹æ³•ã¯ï¼Œç„¡ä½œç‚ºæŠ½å‡ºæ³•ã¨é•ã£ã¦æ¨™æœ¬èª¤å·®ãªã©ãŒã©ã®ãã‚‰ã„ã‚ã‚‹ã‹ã‚ã‹ã‚‰ãªã„ç‚¹ã§é›£ç‚¹ãŒã‚ã‚‹ã€‚
bluesky0804 2017/07/29
æ¨™æœ¬èª¿æŸ»ã«ãŠã‘ã‚‹æ¨™æœ¬æŠ½å‡ºæ³•ã®ä¸€ã¤ã§ï¼Œæ¯é›†å›£ã‚’ã§ãã‚‹ã ã‘ã‚ˆãä»£è¡¨ã™ã‚‹ã‚ˆã†ãªæ¨™æœ¬ã‚’æ„å›³çš„ã«é¸ã³å‡ºã™æ–¹æ³•ã€‚

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
è¦‹ã›ã‹ã‘ã®å›žå¸° - Wikiwand
bluesky0804 2017/07/13
å˜ä½æ ¹éŽç¨‹ã¨å‘¼ã°ã‚Œã‚‹æ™‚ç³»åˆ—å¤‰æ•°åŒå£«ã®å›žå¸°åˆ†æžã«ã‚ˆã£ã¦èµ·ã“ã‚‹å•é¡Œã§ã‚ã‚Šã€å˜ä½æ ¹éŽç¨‹ã¯çµŒæ¸ˆãƒ‡ãƒ¼ã‚¿ãªã©ã§é »ç¹ã«ã¿ã‚‰ã‚Œã‚‹ãŸã‚ã€1980å¹´ä»£ä»¥é™ã®è¨ˆé‡çµŒæ¸ˆå¦ã«ãŠã‘ã‚‹æ™‚ç³»åˆ—åˆ†æžã§ã¯å¸¸ã«æ³¨æ„ãŒæ‰•ã‚ã‚Œã‚‹å•é¡Œã¨ãªã£ã¦ã„ã‚‹ã€‚

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
å˜ä½æ ¹ - Wikiwand
bluesky0804 2017/07/13
å˜ä½æ ¹ãŒã‚ã‚Œã°ä¸€éšŽéšŽå·®ã‚’ã¨ã‚Šã¾ã—ã‚‡ã†ã¨ã„ã†è©±ï¼šã‚‚ã—ç·šå½¢ãªç¢ºçŽ‡éŽç¨‹ã®ç‰¹æ€§æ–¹ç¨‹å¼ã®æ ¹ã®ä¸€ã¤ãŒ1ã§ã‚ã‚‹ãªã‚‰ã°ã€ãã®ç¢ºçŽ‡éŽç¨‹ã¯å˜ä½æ ¹ã‚’æŒã¤ã€‚ã“ã®ã‚ˆã†ãªç¢ºçŽ‡éŽç¨‹ã¯éžå®šå¸¸ã§ã‚ã‚‹ã€‚ã‚‚ã—ã“ã®ç¢ºçŽ‡éŽç¨‹ã®ç‰¹æ€§æ–¹ç¨‹å¼ã®ä»–ã®

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
Winsorizing - Wikiwand
bluesky0804 2017/06/27
for example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile.

economics

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
ã‚¸ãƒƒãƒ—ã®æ³•å‰‡ - Wikipedia
ã‚¦ã‚£ã‚ãƒšãƒ‡ã‚£ã‚¢ï¼ˆ30ãƒ¶å›½èªžç‰ˆï¼‰ã«ãŠã‘ã‚‹å˜èªžã®å‡ºç¾é »åº¦ ã‚¸ãƒƒãƒ—ã®æ³•å‰‡ï¼ˆã‚¸ãƒƒãƒ—ã®ã»ã†ããã€Zipf's lawï¼‰ã‚ã‚‹ã„ã¯ã‚¸ãƒ•ã®æ³•å‰‡ã¨ã¯ã€å‡ºç¾é »åº¦ãŒ k ç•ªç›®ã«å¤§ãã„è¦ç´ ãŒã€1ä½ã®ã‚‚ã®ã®é »åº¦ã¨æ¯”è¼ƒã—ã¦ 1/k ã«æ¯”ä¾‹ã™ã‚‹ã¨ã„ã†çµŒé¨“å‰‡ã§ã‚ã‚‹ã€‚Zipf ã¯ã€Œã‚¸ãƒ•ã€ã¨èªã¾ã‚Œã‚‹ã“ã¨ã‚‚ã‚ã‚‹ã€‚ã¾ãŸã€ã“ã®æ³•å‰‡ãŒæ©Ÿèƒ½ã™ã‚‹ä¸–ç•Œã‚’ã€Œã‚¸ãƒ•æ§‹é€ ã€ã¨è¨˜ã™ã‚‹è«–è€…ã‚‚ã„ã‚‹ã€‚ åŒ…æ‹¬çš„ãªç†è«–çš„èª¬æ˜Žã¯ã¾ã æˆåŠŸã—ã¦ã„ãªã„ã‚‚ã®ã®ã€æ§˜ã€…ãªç¾è±¡ã«é©ç”¨ã§ãã‚‹ã“ã¨ãŒçŸ¥ã‚‰ã‚Œã¦ã„ã‚‹ã€‚ã“ã®æ³•å‰‡ã«å¾“ã†ç¢ºçŽ‡åˆ†å¸ƒï¼ˆé›¢æ•£åˆ†å¸ƒï¼‰ã‚’ã‚¸ãƒƒãƒ—åˆ†å¸ƒã¨ã„ã†ã€‚ã‚¸ãƒƒãƒ—åˆ†å¸ƒã¯ã‚¼ãƒ¼ã‚¿åˆ†å¸ƒï¼ˆè‹±èªžç‰ˆï¼‰ã®ç‰¹æ®Šãªå½¢ã§ã‚ã‚‹ã€‚ ã“ã®æ³•å‰‡ã¯ã‚¢ãƒ¡ãƒªã‚«ã®è¨€èªžå¦è€…ã‚¸ãƒ§ãƒ¼ã‚¸ãƒ»ã‚ãƒ³ã‚°ã‚ºãƒªãƒ¼ãƒ»ã‚¸ãƒƒãƒ—ã«å¸°ã›ã‚‰ã‚Œã¦ã„ã‚‹ã€‚ã‚¸ãƒƒãƒ—ä»¥å‰ã«ä¼¼ãŸè¦³å¯Ÿã‚’ã—ã¦ã„ãŸå…ˆè¡Œç ”ç©¶ã¨ã—ã¦Felix Auerbachï¼ˆè‹±èªžç‰ˆï¼‰ã€Jean-Baptiste Estoupï¼ˆãƒ•ãƒ©ãƒ³ã‚¹èªžç‰ˆï¼‰ãªã©ã®ç ”ç©¶ãŒã‚ã‚Šã€ã‚¸ãƒƒãƒ—è‡ªèº«ã‚‚ãã®ã“ã¨ã‚’1942å¹´
bluesky0804 2017/03/31
ã‚¸ãƒƒãƒ—ã®æ³•å‰‡ï¼ˆã‚¸ãƒƒãƒ—ã®ã»ã†ããã€Zipf's lawï¼‰ã‚ã‚‹ã„ã¯ã‚¸ãƒ•ã®æ³•å‰‡ã¨ã¯ã€å‡ºç¾é »åº¦ãŒk ç•ªç›®ã«å¤§ãã„è¦ç´ ãŒå…¨ä½“ã«å ã‚ã‚‹å‰²åˆãŒ1/k ã«æ¯”ä¾‹ã™ã‚‹ã¨ã„ã†çµŒé¨“å‰‡ã§ã‚ã‚‹ã€‚

çµ±è¨ˆ
ãƒªãƒ³ã‚¯
1